Can I make curve on a path?
You can do it, and using your path, by you'll need to use the path to deform another mesh object, rather than using your path directly as geometry.

Here, I start by making a straight cylinder, with sufficient loops (some provided by CC subdivision) to be able to deform around a curve.
I then give it a curve modifier to deform it in one axis, to give it the U shape you want.  This requires creating another path to define the curvature of your U.
Then I give it another curve modifier, to follow the main path.  The U curvature acquired from the first curve modifier remains.
Curve modifiers can be tricky for those starting out, and I'd recommend researching them more if you have trouble.  You'll want to have a good understanding of a single curve modifier before trying to use two in conjunction, like I'm doing here.  In my picture, I've set my curves to bounds clamp and stretch in properties/object data/shape.
What about your original curve's bevel?  This is now represented by the diameter (and vertex density) of the original mesh that is getting curved.  You can adjust this either by scaling that mesh in edit mode, or by adjusting the scale of individual curve controls.